%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC182-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:26 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 50
% Syntax : Number of formulae : 116 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 803 ( 131 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1261 ( 621 ~; 566 |; 0 &)
% ( 74 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 247 ( 223 !; 0 ?; 247 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( nil = sk3 )
<=> ( nil = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
nil = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = nil,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 )
<=> ( app(app(sk6,cons(sk5,nil)),sk7) = sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(10,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
app(app(sk6,cons(sk5,nil)),sk7) = nil,
inference(transitivity,[status(thm)],[10,7,4]) ).
tff(12,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(14,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(21,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(27,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[30,27,24,14]) ).
tff(32,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(34,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(41,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ssList(cons(sk5,nil))
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6) )
<=> ( ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk6) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
ssList(app(sk6,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[50,44,34,31]) ).
tff(52,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(54,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ( nil = app(sk6,cons(sk5,nil)) )
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ( nil = app(sk6,cons(sk5,nil)) )
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( ~ ssList(app(sk6,cons(sk5,nil)))
| ( nil = app(sk6,cons(sk5,nil)) )
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) )
<=> ( ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ( nil = app(sk6,cons(sk5,nil)) )
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ( nil = app(sk6,cons(sk5,nil)) )
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ( nil = app(sk6,cons(sk5,nil)) )
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ( nil = app(sk6,cons(sk5,nil)) )
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ( nil = app(sk6,cons(sk5,nil)) )
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ( nil = app(sk6,cons(sk5,nil)) )
| ~ ssList(sk7)
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ( nil = app(sk6,cons(sk5,nil)) )
| ( app(app(sk6,cons(sk5,nil)),sk7) != nil ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
nil = app(sk6,cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[70,64,54,51,11]) ).
tff(72,plain,
app(sk6,cons(sk5,nil)) = nil,
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( memberP(app(sk6,cons(sk5,nil)),sk5)
<=> memberP(nil,sk5) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( memberP(nil,sk5)
<=> memberP(app(sk6,cons(sk5,nil)),sk5) ),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
( ~ memberP(nil,sk5)
<=> ~ memberP(app(sk6,cons(sk5,nil)),sk5) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [U: $i] :
rewrite(( ( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ memberP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,axiom,
! [U: $i] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
tff(82,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ memberP(nil,U) )
| ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
~ memberP(nil,sk5),
inference(unit_resolution,[status(thm)],[88,85,14]) ).
tff(90,plain,
~ memberP(app(sk6,cons(sk5,nil)),sk5),
inference(modus_ponens,[status(thm)],[89,75]) ).
tff(91,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(( ( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(97,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(98,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(U,cons(V,W)))
| ~ ssList(U)
| ~ ssItem(V)
| memberP(app(U,cons(V,W)),V)
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[97,96]) ).
tff(99,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(transitivity,[status(thm)],[98,95]) ).
tff(100,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X )
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
( ( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) )),
inference(bind,[status(th)],[]) ).
tff(101,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| memberP(X,V)
| ~ ssList(W)
| ( app(U,cons(V,W)) != X ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(U,cons(V,W)) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(X)
| memberP(X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause175) ).
tff(104,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[104,93]) ).
tff(106,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) ),
inference(modus_ponens,[status(thm)],[106,92]) ).
tff(108,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6)
| memberP(app(sk6,cons(sk5,nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6)
| memberP(app(sk6,cons(sk5,nil)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(app(sk6,cons(sk5,nil)))
| memberP(app(sk6,cons(sk5,nil)),sk5) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6)
| memberP(app(sk6,cons(sk5,nil)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(app(sk6,cons(sk5,nil)))
| memberP(app(sk6,cons(sk5,nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6)
| memberP(app(sk6,cons(sk5,nil)),sk5) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(app(sk6,cons(sk5,nil)))
| memberP(app(sk6,cons(sk5,nil)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6)
| memberP(app(sk6,cons(sk5,nil)),sk5) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(app(sk6,cons(sk5,nil)))
| memberP(app(sk6,cons(sk5,nil)),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(app(U,cons(V,W)))
| memberP(app(U,cons(V,W)),V) )
| ~ ssList(nil)
| ~ ssItem(sk5)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk6)
| memberP(app(sk6,cons(sk5,nil)),sk5) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ ssList(app(sk6,cons(sk5,nil)))
| memberP(app(sk6,cons(sk5,nil)),sk5) ),
inference(unit_resolution,[status(thm)],[113,27,107,14,34]) ).
tff(115,plain,
memberP(app(sk6,cons(sk5,nil)),sk5),
inference(unit_resolution,[status(thm)],[114,51]) ).
tff(116,plain,
$false,
inference(unit_resolution,[status(thm)],[115,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC182-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:32:33 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------